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Projective surjectivity of quadratic stochastic operators on l1 and its application

Mukhamedov, F. and Khakimov, O. and Embong, A. F. (2021) Projective surjectivity of quadratic stochastic operators on l1 and its application. Chaos, Solitons and Fractals, 148 . ISSN 0960-0779

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Official URL: http://dx.doi.org/10.1016/j.chaos.2021.111034

Abstract

A nonlinear Markov chain is a discrete time stochastic process whose transitions depend on both the current state and the current distribution of the process. The nonlinear Markov chain over an infinite state space can be identified by a continuous mapping (the so-called nonlinear Markov operator) defined on a set of all probability distributions (which is a simplex). In the present paper, we consider a continuous analogue of the mentioned mapping acting on L1-spaces. Main aim of the current paper is to investigate projective surjectivity of quadratic stochastic operators (QSO) acting on the set of all probability measures. To prove the main result, we study the surjectivity of infinite dimensional nonlinear Markov operators and apply them to the projective surjectivity of the considered QSO. Furthermore, the obtained results are applied to the existence of the positive solution of some Hammerstein integral equations.

Item Type:Article
Uncontrolled Keywords:nonlinear equation, projective surjection, quadratic stochastic operator
Subjects:Q Science > QA Mathematics
Divisions:Science
ID Code:94255
Deposited By: Narimah Nawil
Deposited On:31 Mar 2022 14:45
Last Modified:31 Mar 2022 14:45

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